Complex Growth of Benzamide Form I: Effect of Additives, Solution Flow, and Surface Rugosity

Understanding crystal growth kinetics is of great importance for the development and manufacturing of crystalline molecular materials. In this work, the impact of additives on the growth kinetics of benzamide form I (BZM-I) crystals has been studied. Using our newly developed crystal growth setup for the measurement of facet-specific crystal growth rates under flow, BZM-I growth rates were measured in the presence of various additives previously reported to induce morphological changes. The additives did not have a significant impact on the growth rates of BZM-I at low concentrations. By comparison to other systems, these additives could not be described as “effective” since BZM-I showed a high tolerance of the additives’ presence during growth, which may be a consequence of the type of growth mechanisms at play. Growth of pure BZM-I was found to be extremely defected, and perhaps those defects allow the accommodation of impurities. An alternative explanation is that at low additive concentrations, solid solutions are formed, which was indeed confirmed for a few of the additives. Additionally, the growth of BZM-I was found to be significantly affected by solution dynamics. Changes in some facet growth rates were observed with changes in the orientation of the BZM-I single crystals relative to the solution flow. Of the two sets of facets involved in the growth of the width and length of the crystal, the {10l̅} facets were found to be greatly affected by the solution flow while the {011} facets were not affected at all. Computational fluid dynamics simulations showed that solute concentration has higher gradients at the edges of the leading edge {10l̅} facets, which can explain the appearance of satellite crystals. {10l̅} facets were found to show significant structural rugosity at the molecular level, which may play a role in their mechanism of growth. The work highlights the complexities of measuring crystal growth data of even simple systems such as BZM-I, specifically addressing the effect of additives and fluid dynamics.


Method
Slurries containing an excess of benzamide solids in IPA were prepared in sealed glass vials using the appropriate amounts of additives. The vials were held at 15°C in a temperature-controlled device (Polar Bear Plus Crystal, Cambridge Reactor Design) for 48 h under constant stirring (250 rpm, magnetic stirrer). 5 x 0.5 ml of saturated solutions were then retrieved with the aid of a syringe, filtered (0.45 μm filter) and added to five independent vials. The mass of the vials and solutions was recorded using an analytical balance (Fisher scientific, ±0.0001g). The samples were then left to evaporate in a vacuum oven (40°C) for over 24 hours. After all solvent had evaporated, the masses of the residual solids were recorded, and the average solubility calculated from the five independent measurements. For the samples containing additives, five independent sets of slurries were prepared, each containing a different BZM: additive ratio. Since the amounts of additives used were small (between 0.1 to 10 mol% on total amount of BM in the slurry), it was assumed that the additives fully dissolved in the saturated solutions from this the theoretical mol% of additive w.r.t the mols of BNZ in the saturated solution is calculated. This was confirmed experimentally by analysing the excess solids from the slurries (DSC and pXRD) which corresponded to pure BZM form I in all cases except at high levels of pTAM (over 18 mol %) and oTAM (over 10 mol%) (ESI). Knowing the original amount of additive the ratio of additive to BZM was then calculated after obtaining the total mass of solids from the equilibrated solution after the solvent had evaporated. For each additive a solubility curve is plotted and trend line fitted

Image Processing
In this work we encounter crystals that show uneven growth across a facet resulting in perturbations and satellite crystals growing from the bulk crystal. In these cases the, convexhull, shape closing method used in our code (detailed in previous work 1 ) will not provide an accurate representation of the crystal shape ( Figure ESI-5). A different method for isolating the crystal shape must be used, Figure ESI-5 shows the original image and the results of closing the shape using three different methods. Two approaches can be used to do this: a morphological closing can be used in which a shape of set size is used to outline and close the shape. Alternatively, we can avoid the shape closing step by adjusting the binarization so that the crystals full outline is visible in the binary image, filling all shapes in the image (the crystal and noise) the crystal shape is picked out based on its area and solidity (area/convex hull area). This method is used in preference as it does not alter the shape outline. However to be used the complete crystal outline must be distinguishable from the background and in some cases this is not possible this method also required the threshold used for binarization to be optimised prior to analysis.

Figure ESI-5.
Example of three different methods for obtaining the crystal shape: the convexhull method, picking the shape based on its area and solidity and using a morphological structuring element to close the shape.

Additional Growth Rate Data
Growth rate data collected for BZM-I grown in the presence of 0.5 mol% pTAM and mTAM is shown below. Growth rate measurements were performed in the presence of 0.5 mol% toluamide due to nucleation on the crystal surface seen at higher doping levels most prevalent for pTAM.  Error bars are seen in pTAM growth rate data while with mTAM growth rate data flows a much smother trend, these observations agree with the slow cooling data.

Computational Fluid Dynamics Calculations
The   The flow domain was discretized with 4.7 thousand quadrilateral finite volume elements with variable size. The grid was refined close to the walls of the crystal, where higher gradients of concentration were expected. Mesh independence tests showed that the adopted mesh was sufficiently refined to resolve both the flow and concentration fields.
The governing equations for the flow and mass transport were numerically solved with the opensource Finite Volume CFD code OpenFOAM v9. 3 Steady-state solutions of the flow and concentration fields were obtained with the solver simpleFoam using second-order interpolation schemes for the advective terms of the governing equations. The SIMPLE method was used to solve iteratively the velocity and pressure fields. The simulations were considered converged when the residuals of all the equations reached values smaller than 10 #$ during the iterative solution process.